For certain complex motor tasks, humans may experience the frustration of a lack of improvement despite repeated practice. We investigate a computational basis for failure of motor learning when there is no prior information about the system to be controlled and when it is not practical to perform a thorough random exploration of the set of possible commands. In this case, if the desired movement has never yet been performed, then it may not be possible to learn the correct motor commands since there will be no appropriate training examples. We derive the mathematical basis for this phenomenon when the controller can be modeled as a linear combination of nonlinear basis functions trained using a gradient descent learning rule on the observed commands and their results. We show that there are two failure modes for which continued training examples will never lead to improvement in performance. We suggest that this may provide a model for the lack of improvement in human skills that can occur despite repeated practice of a complex task.